Get an introduction to precalculus fundamentals

This course is the first of two precalculus courses from the University of Padova, providing you with an introduction to the fundamental mathematical skills required to complete a first course in calculus.

You’ll get familiar with the basic precalculus required for college or undergraduate-level studies, notably: factoring and division; sets and set operations; reasoning and proofs; functions and graphs; and equations and inequalities.

Through this course you’ll gain the foundation to support further mathematical studies, or improve your use of mathematics in everyday life.

0:10Skip to 0 minutes and 10 secondsIf we are going to do this precalculus course, it's going to be really a lot of work. True, but imagine how much we're going to learn in doing this! And I guess those who take the course will learn something too. Who will be taking the course, do you think? Oh, there are lots of people who need such a course, for example those who want to prepare a college course, calculus, say, or statistics, or if you are taking an admission test, to get into business school. And people of good taste who simply want to be better informed about mathematics. And besides, mathematics is good for the brain, and keeps you young also. Oh definitely, look at us!

0:54Skip to 0 minutes and 54 secondsTrue, and lots of people need to brush up on their mathematics. As long as they have some high school maths, they should be able to follow the course. What material would we put into the course, do you think? Well, I suppose we'll put in the basic stuff that people usually know, you know, at the end of high school or beginning university. Things like numbers, the various types. And functions. And their graphs. Some algebra, radicals, how to solve equations... Yes, right! Beautiful stuff! But, algebra? Don't people tend to be intimidated by algebra? I've heard that in some occasions, you know... Personally, I believe algebra is really a lot of fun. Oh, you're right!

1:39Skip to 1 minute and 39 secondsWe'll have to find a way to show them that,once you know a few operations, it's a very natural thing, algebra. Yes, let's hope you can do that in the lectures. But we'll also need to prepare lots of good exercises to go along with those lectures. Yes, and we need to work out how to present problems and solutions in a new and interesting way. Well, if we're gonna do this, we better get started pretty soon...

When would you like to&nbspstart?

What will you&nbspachieve?

Describe the basic arithmetic of numbers, including absolute value and radicals

Identify the standard notation for sets and set operations

Explain the elements of mathematical reasoning and proofs

Classify the types of functions and their graphs

Solve polynomials: roots, factoring, and division

Solve equations and inequalites

Who is the course&nbspfor?

This course is for anyone who wants to brush up on their basic mathematical skills, particularly students in the last year of high school, or at the beginning of undergraduate studies, who intend to take a first course in calculus.

This is a math course. It’s not about the culture or history of math, or its role in society, or about how much fun math can be. The object is to actually learn, to the point of competence, a certain type of elementary but essential mathematics. Sustained effort on the part of the student is an absolute requirement for progress; it could not be otherwise.